NEW YORK — Even as the U.S. Supreme Court debates what is marriage, the sentimental and hugely enjoyable new Broadway musical "Kinky Boots" is debating the nature of manhood, with a fabulous twist. But as timely as this show suddenly seems to be — it posits an ideal world according to Harvey Fierstein, wherein struggle leads to self-acceptance, which leads in turn to public triumph — there's nothing whatsoever that's time-bound about Cyndi Lauper's cheerfully audacious, toe-tapping score.

Lauper, a genuine and necessarily fearless original — happily lassoed for duty on a Great White Way in dire need of a woman with so many melodic hooks in her bag of tricks — has been promoting dance-fueled tolerance for decades. And that distinguished history, judiciously coupled with a book by the famously droll and direct Fierstein, is riveted into the stiletto heels dancing through industrial Britain in this show — a witty, striking and emotionally centered movie-to-musical transfer about a down-at-heel Northampton shoe factory that reinvents itself by making reinforced footwear for hefty drag queens.

It will feel to some as if "Kinky Boots" — which is bound and determined to parallel its two young main characters, Charlie (Stark Sands), the reluctant caretaker of the family shoe business, and Lola (Billy Porter), the drag queen turned shoe designer with a tough past — is a amalgam of "Billy Elliot" and "Priscilla Queen of the Desert."

Sure, but it has taken the best of its predecessors (there's also a dash of "La Cage aux Folles," especially in the relationship of Lola and Charlie) and applied real freshness to familiar formula. Crucially, the style of the production matches the creative identities of the composer and the book writer, both of whom have spent their lives writing of ordinary people who finally cop to their true colors, or realize the rights of others to cover themselves with any material they darn wish.

There is a new determination to Fierstein's writing, peppered as always with pedagogy and comedic sugar. Thankfully, "Kinky Boots" avoids the mushy mid-Atlantic traps that befell the likes of "The Full Monty" (a worker-empowerment movie with a very similar plot to "Kinky Boots"), and it similarly dances away from the hyperkinetic excesses of "Priscilla" and the like (David Rockwell's savvy set is modestly scaled), offering just enough social realism that the world seems always centered in the believable.

Drag queens onstage always do best when there are sharp contrasts, and so it goes here: The director-choreographer Jerry Mitchell, whose work is a clever cocktail of flash, grit and nuance, has cast a plethora of zesty character actors and allowed them to forge not so much a traditional ensemble (no beautiful dancing Amazons here) but a clutch of ordinary assembly-line folk, forced by changing times into opening up their minds. The character roles, most notably Marcus Neville's warm foreman George and Daniel Stewart Sherman's intolerant Don, are unusually weighty.

Lauper's impressively varied numbers — whether it's the ballad "The Soul of a Man" or the danceable "Sex Is the Heel" — are the sting in the tale of "Kinky Boots." Every time the orchestra plays the opening measures, you can feel people leaning into the show, wondering how this new Cyndi Lauper song will sound and feel. If any show could kill the appeal of the jukebox musical, this is that piece. Lauper might be no Adam Guettel, but the weapon of musical surprise has rarely been so deftly wielded.

"Kinky Boots" is also a poster child for the benefits of going out of town. Much crucial work has been done since the Chicago tryout, successful as it was. Most important, the world of the show is now far more consistent and truthful, with prior campy excesses tamed, most contrivances softened and various inauthentic elements shorn (or at least made more credibly British).

Sands, who had yet to find his feet in Chicago, where he was dominated by the enigmatic Porter, now has discovered his way into his character and offers up a genuinely affecting and potent leading performance with a strong emotional center. It was clear in Chicago that the insouciant Annaleigh Ashford, who plays the spunky love interest for Charlie (once he gets rid of his awful fiancee, played by Celina Carvajal, who has a thankless part), was channeling some elements of Lauper in a way that really landed with the audience — and Ashford's quirky influence has only grown.

The wound-tight character played by Porter, whose voice sounded strained at Wednesday's press performance, remains the heart of the show. That's not just because Porter can emote his way through Lauper's cheerfully over-the-top 11o'clock number, "Hold Me in Your Heart," but because his is a performance that seems to cost the actor something — and without that visible price to offset the innate cheeriness and optimism, this show would not work.

"Kinky Boots" is both an idealized escape and a kind of fascinating, even a calming, reflection of the massive social change occurring on both sides of the Atlantic. Much has happened since the 2005 movie was made and, I'll bet, it has arrived more suddenly than even those kinky, old foot soldiers Lauper and Fierstein ever imagined.

You would not exactly tag Cyndi Lauper as one of those old-school composers who work on a Broadway show, see a musical number that's not working, scurry back to their hotel room to stay up all night writing a new song by breakfast, and, that following evening, sit there surviving on coffee...

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